We will focus on the existence of nontrivial, nonnegative solutions to the following quasilinear Schrödinger equation where B1 denotes the unit ball centered at the origin in R2 and g behaves like exp(es4) as s tends to infinity, the growth of the nonlinearity is motivated by a Trudinder-Moser inequality version, which admits double exponential growth. The proof involves a change of variable (a dual approach) combined with the mountain pass theorem.
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- Trudinger-Moser inequality
- double exponential growth
- dual approach
- mountain pass theorem
- quasilinear Schrödinger equation